Probabilistic reasoning and inference for systems biology

Abstract

One of the important challenges in Systems Biology is reasoning and performing hypotheses testing in uncertain conditions, when available knowledge may be incomplete and the experimental data may contain substantial noise. In this thesis we develop methods of probabilistic reasoning and inference that operate consistently within an environment of uncertain knowledge and data. Mechanistic mathematical models are used to describe hypotheses about biological systems. We consider both deductive model based reasoning and model inference from data. The main contributions are a novel modelling approach using continuous time Markov chains that enables deductive derivation of model behaviours and their properties, and the application of Bayesian inferential methods to solve the inverse problem of model inference and comparison, given uncertain knowledge and noisy data. In the first part of the thesis, we consider both individual and population based techniques for modelling biochemical pathways using continuous time Markov chains, and demonstrate why the latter is the most appropriate. We illustrate a new approach, based on symbolic intervals of concentrations, with an example portion of the ERK signalling pathway. We demonstrate that the resulting model approximates the same dynamic system as traditionally defined using ordinary differential equations. The advantage of the new approach is quantitative logical analysis; we formulate a number of biologically significant queries in the temporal logic CSL and use probabilistic symbolic model checking to investigate their veracity. In the second part of the thesis, we consider the inverse problem of model inference and testing of alternative hypotheses, when models are defined by non-linear ordinary differential equations and the experimental data is noisy and sparse. We compare and evaluate a number of statistical techniques, and implement an effective Bayesian inferential framework for systems biology based on Markov chain Monte Carlo methods and estimation of marginal likelihoods by annealing-melting integration. We illustrate the framework with two case studies, one of which involves an open problem concerning the mediation of ERK phosphorylation in the ERK pathway